Gm-C circuits, and, particularly, Gm-C filters, have found widespread application in the design of electronic circuitry. Gm-C filters are especially conspicuous in communications equipment, for example, where they may be utilized in the realization of bandpass filters, VCOs (voltage controlled oscillators), loop filters for PLLs (phase-locked loops), and the like. Principal advantages of Gm-C filters derive from their easy compatibility with prevailing integrated circuit fabrication technology, and from the ability of Gm-C filters to be electronically (and therefore, rapidly) tuned. That is, the center frequency or cutoff frequency of a Gm-C filter may be adjusted electronically by the application of an appropriate control signal (e.g., tuning voltage or signal). The control signal is conventionally applied to either a controllable transconductance or controllable capacitance in the Gm-C filter. As is well known, the transconductance of a Gm-C filter may be controlled by controlling a bias current that flows in an active device, such as a bipolar or MOS (metal oxide semiconductor) transistor. The capacitance of Gm-C filter may be controlled by applying an appropriate tuning voltage to a voltage-dependent capacitance (such as a varactor diode), or by selectively switching fixed, binary-weighted capacitors.
A number of approaches have been deployed to tune Gm-C filters. In accordance with one such approach, the time constant of a “master” Gm-C circuit is quantified by reference to a precision clock signal. During the period of time required for the master Gm-C circuit to charge to a predetermined voltage, the precision clock will output a number of pulses. A control signal is applied to a variable capacitance, or to a variable transconductance, in the master Gm-C circuit so as to cause the number of clock pulses generated during the charging interval to converge to a predetermined number. The control signal is also applied to a variable capacitance, or variable transconductance, in the (“slave”) Gm-C filter circuit.
In general, the tuning precision that may be achieved using the time-constant, pulse-counting tuning method, as alluded to above, is a function, i.e., is inversely proportional to, the number of clock pulses expected to be generated during the charging period. With respect to the above-described approach, it may be demonstrated that the dual objectives of high-speed filter tuning and easily realizable semiconductor device fabrication are mutually antagonistic. For example, if it is assumed that a tuning precision of 5% is required in the target Gm-C filter, and that device geometries are such that readily implemented components in the Gm-C time-constant circuit may present typical transconductance and capacitance values of, respectively, 5 milliohms−1 and 10 pf (picofarads), then a 10 GHz clock is required. A clock signal at this frequency is likely difficult to realize in a standard CMOS (complementary metal/oxide/silicon) process. Alternatively, in order to reduce the clock frequency to 200 MHz, for example, a 500 pf capacitor is required in the Gm-C time-constant circuit. A capacitor of this size occupies a significant amount of semiconductor real estate. Furthermore, processing limitations impose substantial constraints on the degree to which the transconductance, Gm, of the Gm-C time-constant circuit may be reduced (corresponding to an increase in resistance, R). That is, reduction of Gm is contraindicated in designs in which the transconductance element in the Gm-C circuit must be matched to the transconductance in the Gm-C filter.
Accordingly, what is required is an approach to tuning a Gm-C filter, wherein there is achieved satisfactory arbitration of the mutually conflicting constraints that are imposed in order to conform to readily available semiconductor device processing technology.